Question

What are the solutions of :
e. 2(t -1) + 3t < 2
f. 4n +2 < 7(n – 13)
g. 14 – 6n ≤ 2 (7-3n)
h. 4p + 3 > 9p +6 -5p

Answer 1

(e) 2(t - 1) + 3t < 2
2t - 2 + 3t < 2
5t - 2 < 2
5t < 2 + 2
5t < 4
t < 4/5

(f) 4n + 2 < 7(n - 13)
4n + 2 < 7n - 91
4n - 7n < -91 - 2
- 3n < - 93
-3n/-3 < -93/-3
n > 31

(g) 14 - 6n <= 2 (7 - 3n)
14 - 6n <= 14 - 6n
-6n + 6n <= 14 - 14
0 = 0
infinite solutions

(h) 4p + 3 > 9p + 6 - 5p
4p + 3 > 4p + 6
4p - 4p > 6 - 3
0 > 3 (not true)
no solution